Two-dimensional Dirac operator and surface theory

Abstract

We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac operator with periodic coefficients.

82 pages, minor additions

Cited by in corpus (8)

• On organizing principles of Discrete Differential Geometry. Geometry of spheres
• The Moutard transformation for the Davey-Stewartson II equation and its geometrical meaning
• Infinitesimal Darboux transformations of the spectral curves of tori in the four-space
• Surfaces via spinors and soliton equations
• The Moutard transformation of two-dimensional Dirac operators and conformal geometry of surfaces in the four-space
• The quaternionic KP hierarchy and conformally immersed 2-tori in the 4-sphere
• Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional
• Nonlinear Dirac equations on Riemann surfaces